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Unmixed and sequentially Cohen-Macaulay skew tableau ideals

Do Trong Hoang, Thanh Vu

Abstract

We associate a {\it skew tableau ideal} to each filling of a skew Ferrers diagram with positive integers. We classify all unmixed and sequentially Cohen-Macaulay skew tableau ideals. Consequently, we classify all Cohen-Macaulay, Buchsbaum, and generalized Cohen-Macaulay skew tableau ideals.

Unmixed and sequentially Cohen-Macaulay skew tableau ideals

Abstract

We associate a {\it skew tableau ideal} to each filling of a skew Ferrers diagram with positive integers. We classify all unmixed and sequentially Cohen-Macaulay skew tableau ideals. Consequently, we classify all Cohen-Macaulay, Buchsbaum, and generalized Cohen-Macaulay skew tableau ideals.

Paper Structure

This paper contains 3 sections, 24 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Sequentially Cohen-Macaulay skew Ferrers ideals
  3. Skew tableau ideals

Key Result

Theorem 1.3

Let $\lambda = (\lambda_1,\ldots, \lambda_n)$ be a partition. Then $I_\lambda$ is sequentially Cohen-Macaulay if and only if $\lambda$ is saturated.

Theorems & Definitions (62)

  • Definition 1.1
  • Definition 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Definition 1.5
  • Definition 1.6
  • Theorem 1.7
  • Example 1.8
  • Theorem 1.9
  • Theorem 1.10
  • ...and 52 more